Standard deviations cannot be added, the variance (StdDev^2) can be added.

I have seen PT variously interpreted as Part Variation or Process Variation. It is the variation of the parts used in the MSA. Ideally, the variation of these Parts equals the variation of the Process that they came from, so Part Variation should equal Process Variation.

fisrt of all ,i getta say thanks to you all moderators for your replies ,your answers has kind of enlightened me .
yeah, that's what got me confused ,i don't know the exact formula for Total variation , so is the total variation equal to the sum of the three items ,and what does the dots behind mean? is there any more items shall be added to the previous ones ?

and from your words i feel may be in some situation the part variation is not equal to process variation ....right ,so that's the key problem casting me into confusion ......
is that all that i should concern ,i mean the total variation = deviation from process +deviation from measurement system ? and the process variation ideally equals part variation (sometimes at least we should consider the effects from ambience right ?) and the measurement system consists of only two parts : repeatability and reproducibility ?

In the MSA study it is best that parts chosen for the study represent the process.
Keeping this in mind it is very important how you collect the samples for the study.
Like Miner said the variation of the chosen parts should represent the process variation.
A lot of mistakes are made when samples are collected and people just grab 10 pcs from the machine shop to be used in the study. Result is: not enough variation in the parts, resulting in high percentage of EV and AV in relation to the calculated TV together with a very low ndc.

fisrt of all ,i getta say thanks to you all moderators for your replies ,your answers has kind of enlightened me .
yeah, that's what got me confused ,i don't know the exact formula for Total variation , so is the total variation equal to the sum of the three items ,and what does the dots behind mean? is there any more items shall be added to the previous ones ?

and from your words i feel may be in some situation the part variation is not equal to process variation ....right ,so that's the key problem casting me into confusion ......
is that all that i should concern ,i mean the total variation = deviation from process +deviation from measurement system ? and the process variation ideally equals part variation (sometimes at least we should consider the effects from ambience right ?) and the measurement system consists of only two parts : repeatability and reproducibility ?

i appreciate very much ..........

The dots mean that there are other terms that might be added if significant such as an operator x part interaction. This sometimes is a significant part of measurement error, but not always. The ANOVA method breaks it out separately, and the Range method includes it in Repeatability.

The post after your question about part and process variation aswered this nicely.

The measurement system also includes Bias, Linearity and Stability, which includes the effects of ambient conditions.

hi miner ,today i get the formula in MSA handbookTV= process variation/6 (page 116 of MSA manual)as you've listed a formua quoting : [StdDev(total variation)]^2 = [StdDev(process variation)]^2 + [StdDev(repeatability)]^2 + [StdDev(reproducibility)]^2 + ...
so don't you think these two are kind of contradictory of each other
i am new in this field , and easy to get confused ...... thank you

hi miner ,today i get the formula in MSA handbookTV= process variation/6 (page 116 of MSA manual)as you've listed a formua quoting : [StdDev(total variation)]^2 = [StdDev(process variation)]^2 + [StdDev(repeatability)]^2 + [StdDev(reproducibility)]^2 + ...
so don't you think these two are kind of contradictory of each other
i am new in this field , and easy to get confused ...... thank you

These equations are not really in disagreement. The MSA process actually calculates these various components separately, so that you do not see the equation that I provided at one time. However, the MSA calculations are indeed based on this formula.